# [PD] number to fractions external?

Lorenzo Sutton lorenzofsutton at gmail.com
Fri Dec 16 18:38:26 CET 2011

On 16/12/11 16:05, Alexandre Torres Porres wrote:
> looks like a job for an external
Not really answering the OP question but something could be done in Python:

def find_frac(num):
f = float(num)
last_error = 1000
best = (0,0)
for i in xrange(1,1001):
for j in xrange(1,i+1):
divide = (float(i) / float (j))
if divide == f:
return ((i,j),0)
err = abs(divide - f)
if err < last_error:
best = (i,j)
last_error = err
return (best,last_error)

This would try to find the exact fraction or the one with the smallest
error (trying up to 1000/1000). It would return (numerator, denominator,
error). Guess it would work well at least up to 100 but only for
positive numbers... and... not for numbers < 1.. and surely it's not
optimised etc. etc. :)

>>> find_frac(2)
((2, 1), 0)
>>> find_frac(1.5)
((3, 2), 0)
>>> find_frac(1.333333333333333333333333333)
((4, 3), 0)
>>> find_frac(2.4)
((12, 5), 0)
>>> find_frac(2.8)
((14, 5), 0)
>>> find_frac(2.987654321)
((242, 81), 1.234568003383174e-11)
>>> find_frac(50.32)
((956, 19), 0.004210526315787888)
>>> find_frac(50.322)
((956, 19), 0.006210526315790332)
>>> find_frac(50.4)
((252, 5), 0)
>>> find_frac(10.33)
((971, 94), 0.00021276595744623705)
>>> find_frac(10.33333333333333333333333333)
((31, 3), 0)

Lorenzo.
>
>
>
> 2011/12/16 i go bananas <hard.off at gmail.com <mailto:hard.off at gmail.com>>
>
>     actually, i'm not going to do anything more on this.
>
>     i had a look at the articles claude posted, and they went a bit
>
>     my patch will still work for basic things like 1/4 and 7/8, but i
>     wouldn't depend on it working for a serious application.  As you
>     first suggested, it's not so simple, and if you read claude's
>     articles, you will see that it isn't.
>
>     it's not brain science though, so maybe someone with a bit more
>     number understanding can tackle it.
>
>
>
>     On Sat, Dec 17, 2011 at 12:51 AM, Alexandre Torres Porres
>     <porres at gmail.com <mailto:porres at gmail.com>> wrote:
>
>         > i had a go at it
>
>         thanks, I kinda had to go too, but no time... :(
>
>         > yeah, my patch only works for rational numbers.
>
>         you know what, I think I asked this before on this list,
>
>         deja'vu
>
>         > will have a look at the article / method you posted, claude.
>
>         are you going at it too? :)
>
>         by the way, I meant something like 1.75 becomes 7/4 and not
>
>         thanks
>
>         cheers
>
>
>
>         2011/12/16 i go bananas <hard.off at gmail.com
>         <mailto:hard.off at gmail.com>>
>
>             by the way, here is the method i used:
>
>             first, convert the decimal part to a fraction in the form
>             of n/100000
>             next, find the highest common factor of n and 100000
>             (using the 'division method' like this:
>             http://easycalculation.com/what-is-hcf.php )
>
>             then just divide n and 100000 by that factor.
>
>             actually, that means it's accurate to 6 decimal places, i
>             guess.  well...whatever :D
>
>
>
>
>
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